A New Solution to Time Series Inference in Spurious Regression Problems

Phillips (1986) provides asymptotic theory for regressions that relate nonstationary time series including those integrated of order 1, I(1). A practical implication of the literature on spurious regression is that one cannot trust the usual confidence intervals. In the absence of prior knowledge that two series are cointegrated, it is therefore recommended that after carrying out unit root tests we work with differenced or detrended series instead of original data in levels. We propose a new alternative for obtaining confidence intervals based on the Maximum Entropy bootstrap explained in Vinod and Lopez-de-Lacalle (2009). An extensive Monte Carlo simulation shows that our proposal can provide more reliable conservative confidence intervals than traditional, differencing and block bootstrap (BB) intervals.